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# The financial aid office of a certain college has agreed to provide a

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
The financial aid office of a certain college has agreed to provide a  [#permalink]

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29 Sep 2019, 21:03
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:24) correct 31% (02:51) wrong based on 36 sessions

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The financial aid office of a certain college has agreed to provide a $9,000 grant to every student whose total family income (not including the grant) is$22,500 or less. However, for every $40 in family income above this figure, the grant is reduced by$10. If Cedric's award is reduced 40%, what is his family income?

(A) $26,100 (B)$27,000
(C) $31,500 (D)$36,900
(E) $44,100 _________________ Director Joined: 20 Jul 2017 Posts: 887 Location: India Concentration: Entrepreneurship, Marketing WE: Education (Education) Re: The financial aid office of a certain college has agreed to provide a [#permalink] ### Show Tags 30 Sep 2019, 01:05 Bunuel wrote: The financial aid office of a certain college has agreed to provide a$9,000 grant to every student whose total family income (not including the grant) is $22,500 or less. However, for every$40 in family income above this figure, the grant is reduced by $10. If Cedric's award is reduced 40%, what is his family income? (A)$26,100
(B) $27,000 (C)$31,500
(D) $36,900 (E)$ 44,100

$10 grant is reduced for every$40 income higher than 22,500
--> $1 grant is reduced for$4 higher income

Cedric's award is reduced 40%
--> Reduced grant = $$\frac{40}{100}*9000 = 3,600$$
So, Income higher than $$22,500 = 4*3,600 = 14,400$$

--> Total income = $$22,500 + 14,400 = 36,900$$

IMO Option D

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Re: The financial aid office of a certain college has agreed to provide a  [#permalink]

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30 Sep 2019, 16:16
grant value = 9000$award is reduced by 40% he gets ; 3600$
reduced by 5400$; 22500/3600 ; 6.25 value of grant is reduced by this factor total grant value 9000*10/6.25 ; 14,400 answer will be option 14400+22500 ; 36,900 IMO D Bunuel wrote: The financial aid office of a certain college has agreed to provide a$9,000 grant to every student whose total family income (not including the grant) is $22,500 or less. However, for every$40 in family income above this figure, the grant is reduced by $10. If Cedric's award is reduced 40%, what is his family income? (A)$26,100
(B) $27,000 (C)$31,500
(D) $36,900 (E)$ 44,100
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Re: The financial aid office of a certain college has agreed to provide a  [#permalink]

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03 Oct 2019, 12:16
Bunuel wrote:
The financial aid office of a certain college has agreed to provide a $9,000 grant to every student whose total family income (not including the grant) is$22,500 or less. However, for every $40 in family income above this figure, the grant is reduced by$10. If Cedric's award is reduced 40%, what is his family income?

(A) $26,100 (B)$27,000
(C) $31,500 (D)$36,900
(E) $44,100 We see that Cedric received 0.6 x 9,000 =$5,400 in grant, which is $3,600 less than the maximum$9,000 grant. Since 3,600/10 = 360, his family income must be 22,500 + 40 x 360 = 22,500 + 14,400 = \$36,900.

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Re: The financial aid office of a certain college has agreed to provide a   [#permalink] 03 Oct 2019, 12:16
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